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Proof step 100 from proof fsync-dirs (previous step)

icache[m] = mkientry(true, mkinode(m3, md, boolvar, m4, m5, m6)), files0[m] = mkfile(m0, md0, m1, content), m ∈ files0, m ∈ icache, m2 ≤ n * VFS_PAGE_SIZE, m3 ∈ dirs0 ∧ m4 = dirs0[m3].nlink ∧ m6 = dirs0[m3].size ∧ m5 = dirs0[m3].nsubdirs ∧ boolvar ∨ m3 ∈ files ∧ m4 = files[m3].nlink ∧ m5 = 0 ∧ ¬ boolvar ⊦ [fail#(; ; err); asynced := ?; inode := mkinode(m3, md, boolvar, m4, m5, m6); if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}; dirs := dirs0; if err = ESUCCESS then afs_fsync#(inode, false, dirs, files; ; asynced2, err)] (dirs = dirs0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 101:
files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, mkinode(m3, md, boolvar, m4, m5, m6)), files[m3] = mkfile(m7, md1, m8, content0), m ∈ icache, m ∈ files0, m2 ≤ n * VFS_PAGE_SIZE, m3 ∈ dirs0 ∧ m4 = dirs0[m3].nlink ∧ m6 = dirs0[m3].size ∧ m5 = dirs0[m3].nsubdirs ∧ boolvar ∨ m3 ∈ files ∧ m4 = m8 ∧ m5 = 0 ∧ ¬ boolvar ⊦ [fail#(; ; err); asynced := ?; inode := mkinode(m3, md, boolvar, m4, m5, m6); if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}; dirs := dirs0; if err = ESUCCESS then afs_fsync#(inode, false, dirs, files; ; asynced2, err)] (dirs = dirs0)

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files[m3], m7, md1, m8, content0]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files[m3], m7, md1, m8, content0